# Model 5  Split & Fraction Of Work Practice Questions Answers Test With Solutions & More Shortcuts

#### TIME & WORK PRACTICE TEST [7 - EXERCISES]

Question : 1 [SSC CGL Tier-II 2016]

A does \$2/5\$ of a work in 9 days. Then B joined him and they together completed the remaining work in 6 days. B alone can finish the whole work in

a) 8\$2/11\$ days

b) 6\$12/13\$ days

c) 18 days

d) 10 days

Remaining work = 1 - \$2/5 = 3/5\$ parts

(A + B) together do \$3/5\$th part of work in 6 days.

Time taken by A and B in doing whole work

= \${6 × 5}/3\$ = 10 days

A does \$2/5\$th part of work in 9 days.

Time taken by A in doing whole work

= \${9 × 5}/2 = 45/2\$ days

B’s 1 day’s work

= \$1/10 - 2/45 = {9 - 4}/90 = 5/90 = 1/18\$

Required time = 18 days

Question : 2 [SSC CHSL 2015]

If 12 men working 8 hours a day complete the work in 10 days, how long would 16 men working 7\$1/2\$ hours a day take to complete the same work?

a) 6

b) 7

c) 8

d) 10

Using Rule 1,

 Men Working hours Days 12 8 10 ↑ ↑ ↓ 16 7\$1/2\$ x

∴ \${16 : 12}/{15/2 : 8}]\$ : : 10 : x

16 × \$15/2\$ × x = 12 × 8 × 10

8 × 15 × x = 12 × 8 × 10

\$x = {12 × 8 × 10}/{8 × 15}\$ = 8 days

Question : 3 [SSC CGL Tier-II 2015]

x does \$1/4\$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in

a) 9\$3/5\$ days

b) 9 days

c) 7\$1/3\$ days

d) 8\$1/8\$ days

Using Rule 2,

x does \$1/4\$ work in 6 days

x does 1 work in 24 days

Similarly,

y does \$3/4\$ work in12 days

y does 1 work in \${12 × 4}/3\$ = 16 days

(x + y)’s 1 day’s work

= \$1/24 + 1/16 = {2 + 3}/48 = 5/48\$

Required time = \$48/5 = 9{3}/5\$ days

Question : 4 [SSC CHSL 2011]

A does half as much work as B in one-third of the time taken by B. If together they take 10 days to complete a work, then the time taken by B alone to do it would have been

a) 25 days

b) 30 days

c) 12 days

d) 6 days

Using Rule 2,

If B completes a work in x days,

A will complete the same in \${2x}/3\$ days.

\$1/x + 3/{2x} = 1/10\$

\${2 + 3}/{2x} = 1/10\$

2x = 50 ⇒ x = 25 days

Question : 5 [SSC CHSL 2012]

A can do a work in 20 days and B in 40 days. If they work on it together for 5 days, then the fraction of the work that is left is :

a) \$8/15\$

b) \$5/8\$

c) \$1/10\$

d) \$7/15\$

Using Rule 2,

(A + B)’s 5 days’ work = \$5(1/20 + 1/40)\$

= \$5({2 + 1}/40) = 15/40 = 3/8\$

Remaining work = \$1 - 3/8 = 5/8\$

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